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      <h1 class="post-title">传纸条</h1>

      <div class="post-meta">
        <span class="post-time"> 2021-06-01 </span>
        <div class="post-category">
            <a href="/categories/%E7%AE%97%E6%B3%95%E6%8F%90%E9%AB%98%E5%8A%A8%E6%80%81%E8%A7%84%E5%88%92/"> 算法提高动态规划 </a>
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        <li><a href="#思路">思路</a></li>
        <li><a href="#注意">注意</a></li>
        <li><a href="#代码">代码</a></li>
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      <h2 id="思路">思路</h2>
<p>状态表示：f[k, i, j] 表示两个人同时走了k步，第一个人在 (i, k - i) 处，第二个人在 (j, k - j)处的所有走法的最大分值。</p>
<p>状态计算：按照最后一步两个人的走法分成四种情况：</p>
<p>两个人同时向右走，最大分值是 f[k - 1, i, j] + score(k, i, j)；
第一个人向右走，第二个人向下走，最大分值是 f[k - 1, i, j - 1] + score(k, i, j)；
第一个人向下走，第二个人向右走，最大分值是 f[k - 1, i - 1, j] + score(k, i, j)；
两个人同时向下走，最大分值是 f[k - 1, i - 1, j - 1] + score(k, i, j)；
注意两个人不能走到相同格子，即i和j不能相等。</p>
<h2 id="注意">注意</h2>
<p>输出要输出f[n+m] [n] [n],而不是f[n+m] [n] [m];</p>
<p>for循环后要判断，j是不是合法，因为k-i指不定去哪里了。</p>
<h2 id="代码">代码</h2>
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<pre class="chroma"><code class="language-cpp" data-lang="cpp"><span class="cp">#pragma comment(linker, &#34;/STACK:1024000000,1024000000&#34;)
</span><span class="cp">#include</span><span class="cpf">&lt;cstdio&gt;</span><span class="cp">
</span><span class="cp">#include</span><span class="cpf">&lt;cstring&gt;</span><span class="cp">
</span><span class="cp">#include</span><span class="cpf">&lt;algorithm&gt;</span><span class="cp">
</span><span class="cp">#include</span><span class="cpf">&lt;iostream&gt;</span><span class="cp">
</span><span class="cp">#include</span><span class="cpf">&lt;string&gt;</span><span class="cp">
</span><span class="cp">#include</span><span class="cpf">&lt;vector&gt;</span><span class="cp">
</span><span class="cp">#include</span><span class="cpf">&lt;stack&gt;</span><span class="cp">
</span><span class="cp">#include</span><span class="cpf">&lt;bitset&gt;</span><span class="cp">
</span><span class="cp">#include</span><span class="cpf">&lt;cstdlib&gt;</span><span class="cp">
</span><span class="cp">#include</span><span class="cpf">&lt;cmath&gt;</span><span class="cp">
</span><span class="cp">#include</span><span class="cpf">&lt;set&gt;</span><span class="cp">
</span><span class="cp">#include</span><span class="cpf">&lt;list&gt;</span><span class="cp">
</span><span class="cp">#include</span><span class="cpf">&lt;deque&gt;</span><span class="cp">
</span><span class="cp">#include</span><span class="cpf">&lt;map&gt;</span><span class="cp">
</span><span class="cp">#include</span><span class="cpf">&lt;queue&gt;</span><span class="cp">
</span><span class="cp"></span><span class="k">using</span> <span class="k">namespace</span> <span class="n">std</span><span class="p">;</span>
<span class="k">typedef</span> <span class="kt">long</span> <span class="kt">long</span> <span class="n">ll</span><span class="p">;</span>
<span class="k">typedef</span> <span class="kt">unsigned</span> <span class="kt">long</span> <span class="kt">long</span> <span class="n">ull</span><span class="p">;</span>
<span class="cp">#define mst(s,_s) memset(s, _s, sizeof(s))
</span><span class="cp"></span><span class="k">const</span> <span class="kt">double</span> <span class="n">PI</span> <span class="o">=</span> <span class="n">acos</span><span class="p">(</span><span class="o">-</span><span class="mf">1.0</span><span class="p">);</span>
<span class="k">const</span> <span class="kt">double</span> <span class="n">eps</span> <span class="o">=</span> <span class="mf">1e-6</span><span class="p">;</span>
<span class="k">const</span> <span class="kt">int</span> <span class="n">INF</span> <span class="o">=</span> <span class="mh">0x3f3f3f3f</span><span class="p">;</span>
<span class="k">const</span> <span class="kt">int</span> <span class="n">N</span> <span class="o">=</span> <span class="mi">200</span><span class="p">;</span>
<span class="kt">int</span> <span class="n">T</span><span class="p">,</span><span class="n">n</span><span class="p">,</span><span class="n">m</span><span class="p">;</span>

<span class="kt">int</span> <span class="n">a</span><span class="p">[</span><span class="n">N</span><span class="p">][</span><span class="n">N</span><span class="p">],</span><span class="n">f</span><span class="p">[</span><span class="n">N</span><span class="p">][</span><span class="n">N</span><span class="p">][</span><span class="n">N</span><span class="p">];</span>


<span class="kt">int</span> <span class="nf">main</span><span class="p">()</span> <span class="p">{</span>

    <span class="n">cin</span><span class="o">&gt;&gt;</span><span class="n">n</span><span class="o">&gt;&gt;</span><span class="n">m</span><span class="p">;</span>
    <span class="k">for</span><span class="p">(</span><span class="kt">int</span> <span class="n">i</span><span class="o">=</span><span class="mi">1</span><span class="p">;</span><span class="n">i</span><span class="o">&lt;=</span><span class="n">n</span><span class="p">;</span><span class="n">i</span><span class="o">++</span><span class="p">)</span>
        <span class="k">for</span><span class="p">(</span><span class="kt">int</span> <span class="n">j</span><span class="o">=</span><span class="mi">1</span><span class="p">;</span><span class="n">j</span><span class="o">&lt;=</span><span class="n">m</span><span class="p">;</span><span class="n">j</span><span class="o">++</span><span class="p">)</span>
            <span class="n">cin</span><span class="o">&gt;&gt;</span><span class="n">a</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">];</span>
    
    <span class="k">for</span><span class="p">(</span><span class="kt">int</span> <span class="n">k</span><span class="o">=</span><span class="mi">2</span><span class="p">;</span><span class="n">k</span><span class="o">&lt;=</span><span class="n">n</span><span class="o">+</span><span class="n">m</span><span class="p">;</span><span class="n">k</span><span class="o">++</span><span class="p">)</span>
    <span class="p">{</span>
        <span class="k">for</span><span class="p">(</span><span class="kt">int</span> <span class="n">i1</span><span class="o">=</span><span class="mi">1</span><span class="p">;</span><span class="n">i1</span><span class="o">&lt;=</span><span class="n">n</span><span class="p">;</span><span class="n">i1</span><span class="o">++</span><span class="p">)</span>
        <span class="p">{</span>
            <span class="k">for</span><span class="p">(</span><span class="kt">int</span> <span class="n">i2</span><span class="o">=</span><span class="mi">1</span><span class="p">;</span><span class="n">i2</span><span class="o">&lt;=</span><span class="n">n</span><span class="p">;</span><span class="n">i2</span><span class="o">++</span><span class="p">)</span>
            <span class="p">{</span>
                <span class="kt">int</span> <span class="o">&amp;</span><span class="n">v</span><span class="o">=</span><span class="n">f</span><span class="p">[</span><span class="n">k</span><span class="p">][</span><span class="n">i1</span><span class="p">][</span><span class="n">i2</span><span class="p">];</span>
                <span class="kt">int</span> <span class="n">j1</span><span class="o">=</span><span class="n">k</span><span class="o">-</span><span class="n">i1</span><span class="p">,</span><span class="n">j2</span><span class="o">=</span><span class="n">k</span><span class="o">-</span><span class="n">i2</span><span class="p">;</span>
                <span class="k">if</span><span class="p">(</span><span class="n">j1</span><span class="o">&gt;</span><span class="n">m</span> <span class="o">||</span> <span class="n">j2</span><span class="o">&gt;</span><span class="n">m</span><span class="p">)</span> <span class="k">continue</span><span class="p">;</span>

                <span class="kt">int</span> <span class="n">w</span><span class="o">=</span><span class="n">a</span><span class="p">[</span><span class="n">i1</span><span class="p">][</span><span class="n">j1</span><span class="p">];</span>
                <span class="k">if</span><span class="p">(</span><span class="n">i1</span><span class="o">!=</span><span class="n">i2</span><span class="p">)</span> <span class="n">w</span><span class="o">+=</span><span class="n">a</span><span class="p">[</span><span class="n">i2</span><span class="p">][</span><span class="n">j2</span><span class="p">];</span>
                <span class="k">if</span><span class="p">(</span><span class="n">j1</span><span class="o">&gt;</span><span class="mi">1</span> <span class="o">&amp;&amp;</span> <span class="n">j2</span><span class="o">&gt;</span><span class="mi">1</span><span class="p">)</span> <span class="n">v</span><span class="o">=</span><span class="n">max</span><span class="p">(</span><span class="n">f</span><span class="p">[</span><span class="n">k</span><span class="o">-</span><span class="mi">1</span><span class="p">][</span><span class="n">i1</span><span class="p">][</span><span class="n">i2</span><span class="p">]</span><span class="o">+</span><span class="n">w</span><span class="p">,</span><span class="n">v</span><span class="p">);</span>
                <span class="k">if</span><span class="p">(</span><span class="n">j1</span><span class="o">&gt;</span><span class="mi">1</span> <span class="o">&amp;&amp;</span> <span class="n">i2</span><span class="o">&gt;</span><span class="mi">1</span><span class="p">)</span> <span class="n">v</span><span class="o">=</span><span class="n">max</span><span class="p">(</span><span class="n">f</span><span class="p">[</span><span class="n">k</span><span class="o">-</span><span class="mi">1</span><span class="p">][</span><span class="n">i1</span><span class="p">][</span><span class="n">i2</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="o">+</span><span class="n">w</span><span class="p">,</span><span class="n">v</span><span class="p">);</span>
                <span class="k">if</span><span class="p">(</span><span class="n">i1</span><span class="o">&gt;</span><span class="mi">1</span> <span class="o">&amp;&amp;</span> <span class="n">i2</span><span class="o">&gt;</span><span class="mi">1</span><span class="p">)</span> <span class="n">v</span><span class="o">=</span><span class="n">max</span><span class="p">(</span><span class="n">f</span><span class="p">[</span><span class="n">k</span><span class="o">-</span><span class="mi">1</span><span class="p">][</span><span class="n">i1</span><span class="o">-</span><span class="mi">1</span><span class="p">][</span><span class="n">i2</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">+</span><span class="n">w</span> <span class="p">,</span><span class="n">v</span><span class="p">);</span>
                <span class="k">if</span><span class="p">(</span><span class="n">i1</span><span class="o">&gt;</span><span class="mi">1</span> <span class="o">&amp;&amp;</span> <span class="n">j2</span><span class="o">&gt;</span><span class="mi">1</span><span class="p">)</span> <span class="n">v</span><span class="o">=</span><span class="n">max</span><span class="p">(</span><span class="n">f</span><span class="p">[</span><span class="n">k</span><span class="o">-</span><span class="mi">1</span><span class="p">][</span><span class="n">i1</span><span class="o">-</span><span class="mi">1</span><span class="p">][</span><span class="n">i2</span><span class="p">]</span><span class="o">+</span><span class="n">w</span><span class="p">,</span><span class="n">v</span><span class="p">);</span>
            <span class="p">}</span>
        <span class="p">}</span>
    <span class="p">}</span>
    <span class="n">cout</span><span class="o">&lt;&lt;</span><span class="n">f</span><span class="p">[</span><span class="n">n</span><span class="o">+</span><span class="n">m</span><span class="p">][</span><span class="n">n</span><span class="p">][</span><span class="n">n</span><span class="p">]</span><span class="o">&lt;&lt;</span><span class="n">endl</span><span class="p">;</span>
    <span class="k">return</span> <span class="mi">0</span><span class="p">;</span>
<span class="p">}</span>
</code></pre></td></tr></table>
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